If be: EC = 3:2, AB: EC = 4:1, then AE: AC: BC =?

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• 1. As shown in the figure, in △ ABC, a = 30 °, B = 45 °, D is on AB, e is on AC, and AE = EC = De, then ad2: BC2 is equal to______ ．
• 2. On Pythagorean theorem The teacher asked the students to go home and prepare a 21cm long wooden stick for use in class. In order to prevent the stick from breaking, Xiao Ming wanted to put it into his pencil case. It is known that Xiao Ming's pencil case is a cuboid 20cm long and 8cm wide. Can the stick prepared by Xiao Ming be put into his pencil case? Note: write down the steps
• 3. It is known that the sum of the two right sides of a right triangle is 5 cm and the hypotenuse is 2 cm, then the area of the right triangle is 2 cm____ .
• 4. If the three sides of a right triangle are A-B, a, a + B and both a and B are positive integers, the length of one side of the triangle may be () A. 61B. 71C. 81D. 91
• 5. In △ ABC, it is known that ∠ cab = 60 °, D and E are points on edges AB and AC respectively, and ∠ AED = 60 °, ed + DB = CE, ∠ CDB = 2 ∠ CDE, then ∠ DCB = () A. 15°B. 20°C. 25°D. 30°
• 6. Corresponding edges of △ ABC ≌ △ CDA, AB and CD, BC and DA, write other corresponding edges and corresponding angles
• 7. Q: ABC × 4 = CDA, how much is ABCD for
• 8. The average number of ABCD is 13.5, the average number of ABC is 12, the average number of BCD is 15, and the average number of CDA is 14?
• 9. Given that OA = (- 1,8) ob = (- 4,1) OC = (1,3) in the rectangular coordinate plane, it is proved that △ ABC is an isosceles triangle
• 10. It is known that, as shown in the figure, OA bisects ∠ BAC, ∠ 1 = ∠ 2
• 11. As shown in the figure, in △ ABC, ∠ C = 90 °, a = 30 ° and ab + BC = 12cm, then the length of the hypotenuse AB is______ cm．
• 12. It is known that on the BC side of the triangle ABC, be = CF is cut to connect AE AF, which means that ab + AC is greater than AE + AF
• 13. E. F is two points on the edge BC of triangle ABC, and be = CF, connecting AE and AF. proof: ab + AC is greater than AE + AF
• 14. Given that the triangle ABC is an equilateral triangle, take points E and F on AC and BC respectively, and AE = CF, be and AF intersect at point D, then ∠ BDF = what The next two questions of this question, the last question of Changjun bilingual mathematics school-based similar triangle judgment 4
• 15. D is the midpoint of BC, AE is equal to one third of AC, if the area of triangle ade is equal to 4, calculate the area of triangle ABC
• 16. In the known triangle ABC, the angle B = 90 °, ab = 3, BC = 4, G is the center of gravity, and the value of BG is obtained
• 17. Difficult math problem: triangle ABC, angle c = 90 degrees, angle a = 30 degrees, triangle C point does not move, rotates counterclockwise, edge AC intersects AB at f point, Triangle ABC, angle c = 90 degrees, angle a = 30 degrees, triangle C point does not move, rotates counter clockwise, edge AC (CD side after rotation) intersects AB at f point, triangle after rotation is CDE. Rotation angle is ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0 ﹤ 0&
• 18. As shown in the figure, in △ ABC, BD bisects ∠ ABC intersection AC at D, CE bisects ∠ ACB intersection AB at e, CE and BD intersection F, connects AF and extends intersection BC at h, FG ⊥ BC at g through F. (1) if ∠ ABC = 45 ° and ∠ ACB = 65 °, calculate the degree of ∠ HFG; (2) according to the law in (1), explore the relationship between ∠ ABC, ∠ ACB and ∠ HFG; (3) try to explore the size relationship between ∠ BFH and ∠ CFG, and explain the reason
• 19. As shown in the figure, in the triangle ABC, angle a = 60 °, BD and CE bisect angle ABC and angle ACB respectively, BD and CE intersect at point O, try to judge the quantitative relationship of be, CD and BC and prove it
• 20. As shown in the figure, in the triangle ABC, ad and AE are the height and the middle line on the edge of BC respectively. AB = 9, AC = 7, BC = 8, find the length of CD, de and AE